# Properties and Operations of Fractions ```Properties and Operations of Fractions:
Where a, b, c, and d are real numbers, variables, or algebraic expressions and b, d ≠0
𝒂𝒂
Equivalent Fractions:
Example:
𝟏𝟏
𝟐𝟐
𝒃𝒃
𝟐𝟐
𝒄𝒄
= 𝒅𝒅 if and only if 𝒂𝒂𝒂𝒂 = 𝒃𝒃𝒃𝒃
= 𝟒𝟒 because (𝟏𝟏) ∗ (𝟒𝟒) = (𝟐𝟐) ∗ (𝟐𝟐)
𝒂𝒂
−𝒂𝒂
Rules of Signs: − 𝒃𝒃 =
𝒃𝒃
𝒂𝒂
−𝒂𝒂
Generate Equivalent Fractions:
Example:
(𝒙𝒙)(𝟑𝟑)
𝒙𝒙
= (𝟐𝟐)(𝟑𝟑) =
𝟐𝟐
𝒂𝒂
= −𝒃𝒃 and −𝒃𝒃 = 𝒃𝒃
𝟑𝟑𝟑𝟑
𝟔𝟔
𝒂𝒂
𝒂𝒂𝒂𝒂
= 𝒃𝒃𝒃𝒃 , 𝒘𝒘𝒘𝒘𝒘𝒘𝒘𝒘𝒘𝒘 𝒄𝒄 ≠ 𝟎𝟎
𝒃𝒃
Add or Subtract with like denominators:
Example:
𝟏𝟏
+
𝟐𝟐
𝟓𝟓𝟓𝟓
𝟐𝟐
=
𝟏𝟏+𝟓𝟓𝟓𝟓
𝟐𝟐
𝒂𝒂
𝒄𝒄
&plusmn; 𝒃𝒃 =
𝒃𝒃
Add or Subtract with unlike denominators:
𝒂𝒂
𝒄𝒄
𝒂𝒂&plusmn;𝒄𝒄
𝒃𝒃
𝒂𝒂𝒂𝒂
𝒄𝒄𝒄𝒄
&plusmn; 𝒅𝒅 = 𝒃𝒃𝒃𝒃 &plusmn; 𝒃𝒃𝒃𝒃 =
𝒃𝒃
𝒂𝒂𝒂𝒂&plusmn;𝒄𝒄𝒄𝒄
𝒃𝒃𝒃𝒃
(find a common denominator by multiplying top and bottom of each part by the other part’s denominator.)
Example:
𝟏𝟏
𝟐𝟐
𝟑𝟑
(𝟓𝟓) 𝟏𝟏
𝒂𝒂
Multiply Fractions:
Example:
𝟑𝟑
(𝟐𝟐) 𝟑𝟑
+ 𝟓𝟓 = (𝟓𝟓) 𝟐𝟐 + (𝟐𝟐) 𝟓𝟓 =
𝟏𝟏
𝒄𝒄
𝒂𝒂𝒂𝒂
(𝟑𝟑)𝟏𝟏
𝒂𝒂
𝒂𝒂
(𝟓𝟓)(𝟐𝟐)
=
𝟓𝟓+𝟔𝟔
𝟏𝟏𝟏𝟏
𝟏𝟏𝟏𝟏
= 𝟏𝟏𝟏𝟏
(multiply top times the top and bottom times the bottom)
∗ = 𝒃𝒃𝒃𝒃
𝒃𝒃 𝒅𝒅
(𝟑𝟑)(𝟏𝟏)
(𝟓𝟓)(𝟏𝟏)+(𝟐𝟐)(𝟑𝟑)
𝟏𝟏
∗ = (𝟓𝟓)(𝟑𝟑) = (𝟑𝟑)𝟓𝟓 = 𝟓𝟓
𝟓𝟓 𝟑𝟑
𝒄𝒄
𝒅𝒅
𝒂𝒂𝒂𝒂
Divide Fractions: 𝒃𝒃 &divide; 𝒅𝒅 = 𝒃𝒃 ∗ 𝒄𝒄 = 𝒃𝒃𝒃𝒃 , 𝒄𝒄 ≠ 𝟎𝟎.
(if it’s division, just reciprocate the fraction you’re dividing by and change it to multiplication.)
Example:
𝟑𝟑
𝟏𝟏
𝟑𝟑
𝟑𝟑
(𝟑𝟑)(𝟑𝟑)
𝟗𝟗
&divide; 𝟑𝟑 = 𝟓𝟓 ∗ 𝟏𝟏 = (𝟓𝟓)(𝟏𝟏) = 𝟓𝟓
𝟓𝟓
Trevor L.A. May 2010
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